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(-3x^4+6x^3-11x^2+5)-(5x^4+2x^3-x)

2 min read Jun 16, 2024
(-3x^4+6x^3-11x^2+5)-(5x^4+2x^3-x)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression: (-3x^4 + 6x^3 - 11x^2 + 5) - (5x^4 + 2x^3 - x).

Understanding the Steps

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.

  2. Combine like terms: Identify terms with the same variable and exponent (e.g., x^4, x^3, x^2, x). Add or subtract their coefficients.

Solving the Expression

Let's apply these steps:

  1. Distribute the negative sign:

    -3x^4 + 6x^3 - 11x^2 + 5 - 5x^4 - 2x^3 + x

  2. Combine like terms:

    (-3x^4 - 5x^4) + (6x^3 - 2x^3) - 11x^2 + x + 5

  3. Simplify:

    -8x^4 + 4x^3 - 11x^2 + x + 5

Final Answer

The simplified form of the polynomial expression (-3x^4 + 6x^3 - 11x^2 + 5) - (5x^4 + 2x^3 - x) is -8x^4 + 4x^3 - 11x^2 + x + 5.

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